Discussion

Explanation:

It can be seen that, if we place the 3 cones in such a way that they touch each other, it will be similar to placing 3 circles touching, with vertices of the cone corresponding to the centers of the circles. The centers of the circle form an equilateral triangle with each side being 2r. A circle that passes through the centers will be the circumcircle to such a triangle. The radius of the circumcircle of an equilateral triangle is $\left(\frac{1}{\sqrt{3}}\right)$ times its side.

Hence, in our case it would be be $\left(\frac{2r}{\sqrt{3}}\right)$ and $\left(\frac{2r}{\sqrt{3}}\right)$ > r, since $\sqrt{3}$ = 1.73 (approx).

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